Distortions of ethyne when complexed with a cuprous or argentous halide: the rotational spectrum of C₂H₂⋯CuF

Abstract

A new molecule C₂H₂⋯CuF has been synthesized in the gas phase by means of the reaction of laser-ablated metallic copper with a pulse of gas consisting of a dilute mixture of ethyne and sulfur hexafluoride in argon. The ground-state rotational spectrum was detected by two types of Fourier-transform microwave spectroscopy, namely that conducted in a microwave Fabry–Perot cavity and the chirped-pulse broadband technique. The spectroscopic constants of the six isotopologues ¹²C₂H₂⋯⁶³Cu¹⁹F, ¹²C₂H₂⋯⁶⁵Cu¹⁹F, ¹³C₂H₂⋯⁶³Cu¹⁹F, ¹³C₂H₂⋯⁶⁵Cu¹⁹F, ¹²C₂D₂⋯⁶³Cu¹⁹F and ¹²C₂D₂⋯⁶⁵Cu¹⁹F were determined and interpreted to show that the molecule has a planar, T-shaped geometry belonging to the molecular point group C_2v, with CuF forming the stem of the T. Quantitative interpretation reveals that the ethyne molecule is distorted when subsumed into the complex in such manner that the C≡C bond lengthens (by δr) and the two H atoms cease to be collinear with the C≡C internuclear line. The H atoms move symmetrically away from the approaching Cu atom of CuF, to increase each *≡C–H angle by δA = 14.65(2)°, from 180° to 194.65(2)°. Ab initio calculations at the explicitly-correlated level of theory CCSD(T)(F12*)/aug-cc-pVTZ lead to good agreement with the experimental geometry. It is shown that similar distortions δr and δA, similarly determined, for four complexes C₂H₂⋯MX (M = Cu or Ag; X = F, Cl or CCH) are approximately linearly related to the energies D_e for the dissociation process C₂H₂⋯MX = C₂H₂ + MX.

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1. Introduction

The coordination of transition metal atoms M, cations M⁺ or polar salts M⁺X⁻ to alkynes and alkenes has been described in terms of the interaction of the π electrons of the latter compounds with the π* orbitals of the metal atom or ion.^1,2 Such interactions achieve importance by virtue of their presence in coordination compounds that feature in hydrogenation and polymerization reactions.³ For that reason, we have recently been investigating systematically a series of simple, gas-phase complexes of the type C₂H₂⋯MX which contain such interactions, where M is a coinage metal atom and X is a halogen atom.^4–6 The advantage of working in the gas phase is that distortions of the alkyne on complex formation are free from lattice or solvent effects and are therefore intrinsic to the interaction of interest. The technique employed in the synthesis of C₂H₂⋯MX complexes is laser ablation of the metal M in the presence of both ethyne and a source of halogen atom X in a preponderating excess of argon gas. The subsequent, rapid supersonic expansion of the mixture into a vacuum cools and stabilizes the product molecules and allows their rotational spectra to be observed. By these methods it has been possible to determine, with all the precision associated with microwave spectroscopy, the geometries of several species^4–6 C₂H₂⋯MX, where MX is AgCl, AgCCH, or CuCl.

In this article, we report the rotational spectra of six isotopologues of C₂H₂⋯Cu–F. The complexes were produced by the laser ablation of metallic copper in the presence of a pulse of ethyne–SF₆–Ar gas mixture and their spectra were detected by two versions of the Fourier-transform microwave technique. Interpretation of the spectroscopic constants thereby determined leads to a precise characterization of the distortion that ethyne undergoes when it is coordinated to CuF. The distortions will be compared with those predicted by an ab initio calculation conducted at the CCSD(T)(F12*)/AVTZ level of theory Such distortions have now been established, both experimentally and ab initio, as accompanying the attachment of C₂H₂ to MX = CuF, CuCl, AgCl and AgCCH (where M is copper or silver, and X = F, Cl or CCH as appropriate). Variations in these distortions with (1) M and (2) X will be considered.

2. Experimental and theoretical methods

Experimental data for C₂H₂⋯CuF and C₂D₂⋯CuF were recorded on a chirped-pulse Fourier transform microwave spectrometer⁷ operating between 7 and 18.5 GHz. The instrument has been previously described in detail.^8,9 A gas sample was prepared containing approximately 1% C₂H₂ (or C₂D₂ as appropriate) and 1% SF₆ balanced in 6 bar argon. The gas mixture then pulsed over a copper target rod which was ablated with a Nd:YAG laser. The gas pulse was subsequently expanded into a vacuum chamber. For these experiments, the pulsed nozzle was placed perpendicular to the axis of microwave propagation. During each sample injection cycle, 8 free induction decays (FID's) were measured, each 20 μs in duration. For C₂H₂⋯CuF a total of 480 k FID's were acquired (16 h), for C₂D₂⋯CuF the total was 780 k (26 h), and 720 k (24 h) for ¹³C₂H₂–CuF. In each case, Fourier transformation used a digital Kaiser–Bessel window function.

For ¹²C₂H₂⋯CuF, data were also recorded on a Balle–Flygare cavity spectrometer,^10,11 with an equivalent gas sample. These measurements were acquired with the pulsed nozzle placed coaxial with the direction of microwave propagation. Transitions measured in this arrangement appear as Doppler doublets, each normally with a full-width half maximum (FWHM) of 5 kHz (but see Section 3.1); this is compared to a FWHM of approximately 150 kHz for the perpendicular arrangement found in the broadband instrument. Only samples containing isotopes in natural abundance were employed when using this spectrometer.

Geometry optimizations were performed using CCSD(T)(F12*),¹² a coupled-cluster method with single and double excitations, explicit correlation,¹³ and a perturbative treatment of triple excitations.¹⁴ An AVTZ basis set combination was used, by which we mean that the aug-cc-pVTZ basis sets¹⁵ were used for the C, F and H atoms and the aug-cc-pVTZ-PP basis for Cu, in combination with the ECP-10-MDF effective core potential on Cu to account for scalar relativistic effects.^16,17 The frozen-core approximation was used throughout, and all calculations were performed using the MOLPRO package.¹⁸ The equilibrium dissociation energy D_e for the process C₂H₂⋯Cu–F = C₂H₂ + Cu–F was also computed at the CCSD(T)(F12*)/AVTZ level using the counterpoise correction method¹⁹ where, for numerical stability, the CABS singles correction was not included in the correction term. The result was D_e = 170 kJ mol⁻¹.

For the free CuF, the bond length was optimised on a series of potential curves including successive corrections for core correlation, computed at the CCSD(T) level by using the cc-pwCVQZ basis, full triples at the frozen-core level with a cc-pVQZ basis and perturbative quadruples using the cc-pVTZ basis, following a similar procedure to that employed by Gauss et al.²⁰ Post CCSD(T) calculations were performed using the MRCC program²¹ and yielded the fully corrected bond length r_e(Cu–F) = 1.7430 Å, with a basis set uncertainty of 0.0006 Å. This result is in good agreement with the experimental value 1.74493 Å calculated from equilibrium rotational constants²² of ⁶³Cu¹⁹F and ⁶⁵Cu¹⁹F by using the expression r_e = {h/8π²μB_e}^½. At the CCSD(T)(F12*)/aug-cc-pVTZ level of theory, as used for C₂H₂⋯Cu–F, the equilibrium bond length for the free CuF molecule is predicted to be 1.7422(25) Å, where the error is that estimated (via gaussian error propagation) to arise from basis set incompleteness (0.0007 Å), core valence correlation error (0.0021 Å) and higher-order correlation (0.0011 Å).

3. Results

3.1 Determination of spectroscopic constants

For all six isotopologues investigated, only vibrational ground-state, a-type R-branch transitions with K₋₁ = 0 or 1 of the asymmetric-rotor complex C₂H₂⋯Cu–F were observed under the experimental conditions described in Section 2. Each transition carried a resolvable nuclear quadrupole hyperfine structure resulting from a single quadrupolar nucleus ⁶³Cu or ⁶⁵Cu (I = 3/2). Transition frequencies of each isotopologue were fitted by means of the program PGOPHER²³ with the following choice of Hamiltonian:

H = H_R − ⅙Q(Cu): ∇E(Cu), (1)

in which Q(Cu) and ∇E(Cu) are the Cu nuclear electric quadrupole tensor and the electric field gradient tensor at the Cu nucleus, respectively. H_R is the familiar Hamiltonian for a semi-rigid, asymmetric-rotor molecule and contains both rotational constants and centrifugal distortion constants. The H matrix was constructed in the coupled symmetric rotor basis, with the Watson A reduction²⁴ chosen for H_R, In addition to the rotational constants, H_R contains terms involving the five quartic centrifugal distortion constants Δ_J, Δ_JK, Δ_K, δ_J, and δ_K.

The rotational constants of the most abundant isotopologue ¹²C₂H₂⋯⁶³Cu¹⁹F are large enough that only one group of J + 1 → J transitions, namely that with J = 1, could be measured in the frequency range available. A set of internally consistent arguments will be presented to show that the geometry of C₂H₂⋯Cu–F is of the planar, T-shaped type in which the non-covalent interaction of the two component molecules involves primarily the Cu atom of CuF and the π bond of ethyne, as shown in Fig. 1. The experimental consequences of such a geometry are as follows:

Fig. 1 The geometry (drawn to scale) of C₂H₂⋯Cu–F determined from analysis of the rotational spectra of six isotopologues. The atoms are coplanar and the principal inertia axis a coincides with the C₂ axis of symmetry. The ethyne subunit is significantly distorted relative to the free molecule, both in respect of the angle A and of the distance r(C≡C). See text for discussion of the detailed geometry.

(1) The molecule is a nearly prolate, planar asymmetric rotor of molecular point group C_2v, with the a axis coincident with the C₂ axis. The rotational constant A₀ is close in magnitude to the rotational constant B₀ of free ethyne. Any difference of the two rotational constants will provide quantitative information about the extent of any geometrical distortion of the ethyne molecule when subsumed into C₂H₂⋯Cu–F.

(2) The ground-state molecule will have a small positive inertia defect

Δ₀ = I⁰_c − I⁰_b − I⁰_a, (2)

which is an important criterion of molecular planarity.

(3) A rotation C^a₂ exchanges a pair of equivalent protons (I = 1/2) and this endows K₋₁ = 1 transitions with a nuclear spin statistical weight of 3 relative to that of 1 for K₋₁ = 0 transitions. This effect is evident in the set of 2₁₂ → 1₁₁, 2₀₂ → 1₀₁, 2₁₁ → 1₁₀ transitions, as can be seen from the recording of these transitions shown in Fig. 2. Similar arguments applied to the ¹²C₂D₂⋯Cu¹⁹F and ¹³C₂H₂⋯Cu¹⁹F isotopologues require the corresponding ratios to be 1 : 2 and 6 : 10, respectively, which were indeed as observed.

Fig. 2 A recording (10 × vertical magnification) of the three J = 2 → 1 transitions of ¹²C₂H₂⋯⁶³Cu¹⁹F and ¹²C₂H₂⋯⁶⁵Cu¹⁹F, showing Cu nuclear quadrupole hyperfine structure (upper panel). The downward pointing spectrum is that synthesized by using PGOPHER and the spectroscopic constants given in Table 1 (2 K rotational temperature assumed). This simulation does not include nuclear spin statistics, so the difference between the simulation and observed spectrum shows clearly the presence of nuclear spin statistics in the latter. Even though hyperfine splitting is greater in the two outer transitions 2₁₂ → 1₁₁ and 2₁₁ → 1₁₀, their statistical weight advantage (3 : 1) over the central 2₀₂ → 1₀₁ transition is evident. The lower panel gives an expanded version of the 2₁₂ → 1₁₁ transitions of ¹²C₂H₂⋯⁶³Cu¹⁹F (blue) and ¹²C₂H₂⋯⁶⁵Cu¹⁹F (red). The simulated spectrum (with appropriate scaling of intensities) is again downward pointing.

(4) Isotopic substitution of ⁶³Cu by ⁶⁵Cu should leave A₀ unchanged.

It is evident that the rotational constant A₀ has a central role to play in drawing conclusions about the symmetry and geometry of C₂H₂⋯Cu–F. Unfortunately, the (K₋₁ = 0 or 1) transition frequencies have a very weak dependence on A₀ and it was not possible from the measured transition frequencies to determine A₀ independently of the two centrifugal distortion constants Δ_J and Δ_JK. (There is insignificant dependence on the remaining centrifugal distortion constants.) This difficulty was circumvented by the following approach.

It has been shown elsewhere that centrifugal distortion constants of molecules similar to C₂H₂⋯Cu–F can be calculated ab initio with good accuracy.⁶ For example, in the closely related species C₂H₂⋯Cu–Cl calculations at the MP2/cc-pVTZ level of theory reproduced Δ_J and Δ_JK to within a few standard deviations of the well-determined experimental values. Here, the five quartic constants (Δ_J, Δ_JK, Δ_K, δ_J and δ_JK) for C₂H₂⋯Cu–F were calculated for the optimized geometry at the higher level of theory MP2/aug-cc-pVQZ with the aid of the Gaussian electronic structure package²⁵ for each isotopologue investigated. The calculated constants Δ_J and Δ_JK were then fixed in the PGOPHER²³ fits of observed frequencies to determine the rotational constants A₀, B₀ and C₀ and the Cu nuclear quadrupole coupling constants χ_aa(Cu) and χ_bb(Cu) − χ_cc(Cu) for the isotopologues ¹²C₂H₂⋯⁶³Cu¹⁹F and ¹²C₂H₂⋯⁶⁵Cu¹⁹F in the first instance. The spectroscopic constants so determined both from measurements made with the Balle–Flygare and the chirped-pulse spectrometers are displayed in Table 1. The residuals of the fit to frequencies collected with the Balle–Flygare spectrometer were poorer than the usual few kHz. This arises because C₂H₂⋯CuF carries four nuclei (H, H, Cu and F) with magnetic moments of significant magnitude, in addition to the electric quadrupolar moment of the Cu nucleus. Moreover, only the lowest J transitions were available because of the relatively large rotational constants. The magnetic coupling of these nuclei (Cu, F spin–spin coupling, for example) can lead to further complicated but minor, partially resolved splitting or broadening and/or lineshape distortion of each Cu nuclear quadrupole component and is most significant at the lowest J. Therefore assignment of the magnetic sub-structure was not possible in the observed transitions of C₂H₂⋯CuF, particularly those with K₋₁ = 1, and hence larger than normal residuals in the fit of the Cu nuclear quadrupole hyperfine structure resulted. When measured with the lower resolution, chirped-pulse instrument, fitted frequencies assigned to Cu quadrupole components gave similar magnitude residuals. Reassuringly, the spectroscopic constants determined independently with the two spectrometers are identical within experimental error.

Table 1 Ground-state spectroscopic constants of ¹²C₂H₂⋯^63,65CuF as determined with two different pulsed-jet, Fourier-transform microwave spectrometers (Balle–Flygare and chirped-pulse types)

Spectroscopic constant	Balle–Flygare		Chirped-pulse
	^12C2H2⋯^63CuF	^12C2H2⋯^65CuF	^12C2H2⋯^63CuF	^12C2H2⋯^65CuF
a Values calculated at the MP2/aug-cc-pVQZ level of theory and fixed in the fit. b Number of nuclear quadrupole components included in the fit. c Standard deviation of fit.
A 0/MHz	34 749(83)	34 930(270)	35 030(230)	35 020(180)
B 0/MHz	3431.4407(48)	3430.5201(55)	3431.4404(56)	3430.5159(42)
C 0/MHz	3116.7391(44)	3115.9722(55)	3116.7348(56)	3115.9752(39)
Δ JK /kHz^a	[38.3]	[38.2]	[38.3]	[38.2]
Δ J/kHz^a	[0.61]	[0.61]	[0.61]	[0.61]
χ aa (Cu)/MHz	69.991(47)	64.721(53)	69.979(53)	64.720(40)
{χbb(Cu) − χcc(Cu)}/MHz	−79.17(11)	−73.25(12)	−79.17(13)	−73.224(73)
N	20	16	18	19
σ r.m.s./kHz^c	30	33	34	26

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Measurements for ¹³C₂H₂⋯^63,65Cu¹⁹F, and ¹²C₂D₂⋯^63,65Cu¹⁹F were made exclusively on the chirped-pulse instrument to conserve the more expensive isotopic materials. The spectroscopic constants for these species were obtained in a similar way and are recorded in Table 2. Detailed fits are available as Supplementary Data²⁶ at http://dx.doi.org/xxxxx. The effect of changes in the assumed values of the centrifugal distortion constants were investigated for the isotopologue ¹²C₂H₂⋯⁶³Cu¹⁹F. Changes of 10% in the assumed values of the distortion constants Δ_J and Δ_JK lead to changes in A that are small compared with the errors shown in Table 1. The standard deviations in A₀ values are higher than those identified in other B⋯MX studies because only one J + 1 → J transition is available within the bandwidth of the spectrometer in the present work.

Table 2 Ground-state spectroscopic constants of ¹³C₂H₂⋯^63,65CuF and ¹²C₂D₂⋯^63.65CuF as determined with a chirped-pulse, pulsed-jet, Fourier-transform microwave spectrometer

Spectroscopic constant	^13C2H2⋯^63CuF	^13C2H2⋯^65CuF	^12C2D2⋯^63CuF	^12C2D2⋯^65CuF
a Values calculated at the MP2/aug-cc-pVQZ level of theory and fixed in the fit. b Number of nuclear quadrupole components included in the fit. c Standard deviation of fit.
A 0/MHz	33 250(240)	32 950(290)	25 208(19)	25 156(32)
B 0/MHz	3302.7667(62)	3301.4981(98)	3260.5869(86)	3259.257(14)
C 0/MHz	2996.4700(43)	2995.4204(47)	2881.9524(88)	2880.939(11)
Δ JK /kHz^a	[34.7]	[34.7]	[30.9]	[30.8]
Δ J /kHz^a	[0.56]	[0.56]	[0.53]	[0.53]
χ aa (Cu)/MHz	70.012(59)	64.756(71)	70.051(55)	64.743(56)
{χbb(Cu) − χcc(Cu)}/MHz	−79.23(17)	−73.28(24)	−80.4(38)	−69.8(39)
N	20	15	17	13
σ r.m.s./kHz^c	33.8	32.2	23.7	22.8

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It is significant that values of the A₀ for ¹²C₂H₂⋯⁶³Cu¹⁹F and ¹²C₂H₂⋯⁶⁵Cu¹⁹F (Table 1) are equal within experimental error (as required if Cu lies on the a axis). These values of A₀ and their associated uncertainties strongly imply that the average of the two results provides the most reliable value for this quantity, namely 34 840(90) MHz (where the quoted error is the range about the mean). This value will be used in geometry determinations set out in Section 3.2, together with the mean value A₀ = 33 100(150) MHz for the pair (¹³C₂H₂⋯⁶³Cu¹⁹F, ¹³C₂H₂⋯⁶⁵Cu¹⁹F) and A₀ = 25 182(26) MHz for the pair (¹²C₂D₂⋯⁶³Cu¹⁹F, ¹²C₂D₂⋯⁶⁵Cu¹⁹F). We note that A₀ = 34 840(90) MHz is smaller by 435(90) MHz than the B₀ value of free ¹²C₂H₂ (see Table 3 for various properties of isotopologues of the free molecules ethyne^27,28 and cuprous fluoride²²). Similar conclusions (see Table 2) apply to the pair (¹³C₂H₂⋯⁶³Cu¹⁹F, ¹³C₂H₂⋯⁶⁵Cu¹⁹F), for which the mean decrease from free ¹³C₂H₂ is 464(150) MHz, and the pair (¹²C₂D₂⋯⁶³Cu¹⁹F, ¹²C₂D₂⋯⁶⁵Cu¹⁹F), for which a mean decrease of 236(26) MHz relative to B₀ of free ¹²C₂D₂ is observed. These decreases, although not well determined, indicate a change in the ethyne geometry when it becomes attached to CuF. Moreover, the very small change in all three rotational constants on substitution of ⁶³Cu by ⁶⁵Cu establishes that the Cu atom lies close to the centre of mass and therefore that the order along the a axis is *–Cu–F, where * indicates the centre of the C≡C bond.

Table 3 Some spectroscopic constants and bond lengths of C₂H₂ and CuF referred to in evaluating properties of C₂H₂⋯CuF

Quantity constant	^12C2H2	^13C2H2	^12C2D2	^63Cu^19F	^65Cu^19F
a Ref. 27. b Calculated by fitting the moments of inertia I^0b of ^12C2H2 and ^13C2H2 from ref. 27. See text. c Calculated by fitting the moment of inertia I^0b of ^12C2D2 with r(C≡C) fixed at 1.206553 Å. d Ref. 28. e Ref. 22 .f Calculated from B0 value by using r0 = {h/8π^2μB0}^½, with B0 estimated from Dunham constants in ref. 22.g Calculated from Be value by using re = {h/8π^2μBe}^½ with Be from ref. 22.h Calculated at the CCSD(T)(F12*)/aug-cc-pwCVQZ level of theory, with post-CCSD(T) corrections made for basis set incompleteness, core-valence correlation, and higher-order correlations.
Ethyne				—	—
B 0/MHz	35274.9693(54)^a	33564.005^a	25418.6291^a
Geometry	r 0(C2H2)^b	r 0(C2D2)^c	r e
r(C≡C)/Å	1.206553(6)	(1.206553)	1.20286(3)	—	—
r(C–H)/Å	1.06238(2)	1.06011(3)	1.06166(6)	—	—
Cuprous fluoride				—	—
B 0/MHz^e	—	—	—	11325.8910	11245.2404
B e/MHz^e	—	—	—	11374.2092	11293.0426
r 0(Cu–F)/Å	—	—	—	1.74865^f	1.74863^f
r e(Cu–F)/Å (experiment)	—	—	—	1.74493^g	1.74493^g
r e(Cu–F)/Å (ab initio calc.)	—	—	—	1.7430(3)^h

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The Cu nuclear quadrupole coupling constants are reasonably well determined. The ratio of the values χ_aa(⁶³Cu)/χ_aa(⁶⁵Cu) = 1.0814(16) lies within experimental error of the known ratio²⁹Q(⁶³Cu)/Q(⁶⁵Cu) = 1.0806(3) of the nuclear electric quadrupole moments of the copper nuclides. The large difference between χ_bb(Cu) = −74.58 MHz and χ_cc(Cu) = 4.59 MHz is evidence of a large anisotropy in the electric field gradient at Cu along the b and c principal inertia axis directions arising from the facts that (1) the Cu atom is close to the ethyne π bond and (2) the electron distribution within the triple bond C≡C is different along the two directions. Indeed, the large difference {χ_bb(⁶³Cu) − χ_cc(⁶³Cu)} = −79.17(11) MHz provides convincing evidence of the proximity of Cu to the C≡C bond. In the related molecule C₂H₂⋯Ag–Cl, in which Cl is remote from the ethyne π bond, values of the Cl nuclear quadrupole coupling constants are χ_aa(³⁵Cl) = −28.9268(78) MHz and {χ_bb(³⁵Cl) − χ_cc(³⁵Cl)} = −3.256(7) MHz.

3.2 Molecular geometry

Of the four consequences of a planar geometry of the type shown in Fig. 1, it was indicated in Section 3.1 that three were satisfied by experimental results for C₂H₂⋯Cu–F. The fourth is that the inertia defect, as defined in eqn (2), should be small and positive. If the Cu atom does lie on the a axis, it is reasonable to use the mean I⁰_a value for a pair of isotopologues ^mC₂ⁿH₂⋯⁶³Cu¹⁹F and ^mC₂ⁿH₂⋯⁶⁵Cu¹⁹F in calculating Δ₀ for both members of the pair. The results are Δ₀ = 0.365(38) u Ų and 0.366(38) u Ų for the ¹²C₂H₂⋯^63,65Cu¹⁹F pair, 0.373(69) u Ų and 0.373(69) u Ų for the ¹³C₂H₂⋯^63,65Cu¹⁹F pair, and 0.295(22) u Ų and 0.293(22) u Ų for the ¹²C₂D₂⋯^63,65Cu¹⁹F pair. The very similar values, observed across a similar range of isotopologues, for each of the related planar molecules C₂H₂⋯Cu–Cl⁶ and C₂H₂⋯Ag–Cl⁵ reinforce the conclusion that C₂H₂⋯Cu–F is also planar.

Thus, all the evidence so far presented is consistent with a geometry of C₂H₂⋯CuF of the planar, T-shaped type of C_2v symmetry illustrated in Fig. 1, with the atoms in the indicated order. Quantitative detail of the geometry can be determined experimentally in two ways from the zero-point rotational constants of the six isotopologues of C₂H₂⋯CuF investigated, namely a partial r_s geometry and an almost complete r₀ geometry. These results will be compared with the full r_e geometry obtained from ab initio calculations carried out at the CCSD(T)(F12*/AVTZ) level of theory.

If equilibrium rotational constants (and therefore equilibrium principal moments of inertia) of the various isotopologues of C₂H₂⋯CuF investigated were available, the equilibrium principal-axis co-ordinates a_C, b_C, a_H, and a_Cu could be determined by means of eqn (3)–(5). In view of the molecular planarity and the existence of the symmetry operation C^a₂, the changes I_b and I_a in the equilibrium principal moments of inertia that accompany the double isotopic substitution of X by X′ (X = ¹²C or H; X′ = ¹³C or D, respectively) at symmetrically equivalent atoms are related to the equilibrium coordinates a_X and b_X by the expressions put forward by Chutjian³⁰

|a_X| = (ΔI_b/μ_D)^½, (3)

|b_X| = {ΔI_a/(2Δm)}^½, (4)

in which μ_D = (2ΔmM)/(M + 2Δm) is the reduced mass for the double substitution in the parent isotopologue of mass M leading to a mass change 2Δm. The equilibrium principal axis co-ordinate a_Cu of the atom Cu, which lies on the a-axis of C₂H₂⋯CuF, is given in terms of changes ΔI_b and ΔI_c in equilibrium principal moments of inertia accompanying isotopic substitution at Cu by Kraitchman's equation³¹

|a_Cu| = {(ΔI_b + ΔI_c)/2μ_S}^½, (5)

where μ_S = (ΔmM)/(M + Δm) is the reduced mass for the substitution. When equilibrium quantities are unavailable, Costain^32,33 proposed using zero-point ΔI⁰ values in place of their equilibrium counterparts ΔI^e in eqn (3)–(5) and named the resulting coordinates as substitution or r_s coordinates. The r_s coordinates a_C, b_C, a_H, b_H and a_Cu so obtained from eqn (3)–(5) are given in Table 4. Each refers to the principal inertia axes of ¹²C₂H₂⋯⁶³Cu¹⁹F as the parent molecule and the chosen signs are those that lead to reasonable bond lengths. Note that the mean of A₀ for pairs of ^63,65Cu isotopologues, as given in Section 3.1, were used in the calculation of the b_C and b_H coordinates. The substantial uncertainties in b_C and b_H result from the relatively large errors assigned to A₀. A r_s coordinate a_F is not available because fluorine possesses only one stable isotope and so the value of a_F given in Table 4 was determined, as recommended by Costain,³² from the other r_s coordinates with the aid of the first moment condition,in which the sum over j indicates that all atoms but F are included.

Table 4 Various types of principal inertia axis coordinate and geometry determined for C₂H₂⋯Cu–F

Atom	r s geometry		r 0 geometry		r e geometry^a
	Coordinate^b		Coordinate		Coordinate
	a/Å	b/Å	a/Å	b/Å	a/Å	b/Å
a The re geometry was optimized at the CCSD(T)(F12*)/aug-cc-pVTZ level of theory. b The errors in rs coordinates aX are those given by δa = (0.0015 Å)/a, as suggested by Costain in ref. 32. The errors in rs coordinates bX are those propagated from the poorly determined rotational constants A0. c Assumed value obtained by adding the difference r0(C–H) − re(C–H) = 0.00072 Å of the quantities for free ethyne to re(C–H) calculated for C2H2⋯Cu–F and given in the final column. See text for discussion.
H	−1.9764(8)	±1.663(9)	−1.9767(4)	±1.6587(1)	−1.9762	±1.6501
C	−1.7066(9)	±0.62(4)	−1.7059(4)	±0.6231(1)	−1.6947	±0.6182
Cu	0.142(10)	0.0000	0.1415(3)	0.0000	0.1412	0.0000
F	1.893(33)	0.0000	1.8961(6)	0.0000	1.8803	0.0000

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Distance/angle	rs geometry	r 0 geometry or angle	r e geometry
r(C≡C)/Å	1.24(4)	1.2461(1)	1.2363
r(C–H)/Å	1.077(4)	[1.07041]^c	1.0697
r(Cu–*)/Å	1.85(1)	1.8474(7)	1.8359
r(Cu–F)/Å	1.751(10)	1.7547(9)	1.7392
Angle A/°	194.5(6)	194.65(2)	195.3

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The significantly larger magnitude of a_H than a_C provides experimental evidence that the angular geometry of ethyne is distorted in the manner shown in Fig. 1, that is the H atoms move away from the C≡C internuclear line when the complex is formed, with the two equivalent angles A = ∠H–C≡* (see Fig. 1 for definition) exceeding 180°. The value obtained from the r_s coordinates in Table 3 is A = 194.5(6)° (see Table 4), where the large error is consequent upon the errors in the A₀ values. This distortion is established with greater accuracy in the experimental r₀ and ab initio r_e geometries discussed later (see below). The bond distances implied by the r_s coordinates are also included in Table 4.

When the minimum number of bond lengths and angles required to establish a molecular geometry uniquely is fitted to a sufficient number of zero-point principal moments of inertia by the least-squares method, the result is called a r₀ geometry, i.e one obtained when the rovibrational contributions ε_a = I⁰_a − I^e_a, etc. to the moments of inertia are ignored. A fit of I⁰_b and I⁰_c (values of I⁰_a were excluded because of their relatively low accuracy) of all six isotopologues of C₂H₂⋯Cu–F implied by the rotational constants B₀ and C₀ reported in Tables 1 and 2 to determine r(C≡*), r(*–Cu), r(Cu–F), r(C–H), and A = ∠H–C≡* was unsatisfactory, however, because of high correlation between two last-named quantities. To break the correlation, the following approach was used. A good estimate of r₀(C–H) is given by adding r_e(C–H) of C₂H₂⋯Cu–F from the CCSD(T)(F12*)/AVTZ calculation to the difference r₀(C–H) − r_e(C–H) = 0.00072 Å for free ethyne^27,28 (Table 3), with the result r₀(C–H) = 1.07041 Å. This value was then fixed in the fit. The geometry and principal axis coordinates were then determined under this assumption with the aid of Kisiel's program STRFIT³⁴ and are included in Table 4. There is excellent agreement with the corresponding r_s quantities, given the large error in the b_s coordinates propagated through the rotational constants A₀.

4. Discussion

The new molecule C₂H₂⋯Cu–F has been synthesized by interaction of the plasma produced by laser ablation of a copper rod with a supersonically-expanded pulse of gas containing SF₆ and C₂H₂ diluted with a large excess of argon. It was detected by means of its ground-state rotational spectrum and was shown to have a planar, T-shaped geometry of C_2v symmetry, with the CuF molecule lying along a C₂ axis of the C₂H₂ molecule. Quantitative aspects of the molecular geometry were determined through the investigation of six isotopologues. A significant finding is that the ethyne subunit is considerably distorted by the interaction of its C≡C bond with the Cu atom of CuF. The H atoms move from the C≡C internuclear line, in the direction away from the approaching Cu atom, so that the *≡C–H angle increases from 180° to 194.65(2)°. The C≡C bond lengthens by ca. 0.04 Å. These distortions are well reproduced in the optimized geometry of C₂H₂⋯Cu–F obtained from ab initio calculations carried out at the CCSD(T)(F12*)/AVTZ level of theory (see Table 4).

Similar distortions have now been observed in the series of molecules C₂H₂⋯CuF, C₂H₂⋯AgCl,⁴ C₂H₂⋯AgCCH,⁵ and C₂H₂⋯CuCl,⁶ each of which has the planar T-shaped, C_2v geometry with the metal atom adjacent to the ethyne π bond (see Fig. 1). The changes δA in the angle *≡C–H and δr in the distance r(C≡C) are [14.65(2)°, 4.0(1) pm], [7.70(4)°, 2.86(4) pm], [5.9(1)°, 2.61(3) pm] and [12.5(2)°, 2.7(3) pm] respectively, along the series. The corresponding energy changes D_e accompanying dissociation into C₂H₂ and MX have been calculated ab initio [at the CCSD(T)(F12*)/AVTZ or AVDZ levels] to be 170, 97.5, 92 and 148 kJ mol⁻¹, respectively. Fig. 3 displays a plot of each of δA and δr versus D_e for these molecules. The origin has been included as a point in each plot because when the interaction energy D_e is zero, presumably there is no distortion of the ethyne subunit. Fig. 3 shows that there is an approximate linear relationship between each of the two types of distortion δA and δr and the strength of the interaction D_e.

Fig. 3 Plots of the angular distortion δA (see Fig. 1 for a definition of the angle δA) and the extension δr of the C≡C bond of ethyne on formation of the complexes C₂H₂⋯MX against the energy D_e required for the dissociation reaction C₂H₂⋯MX = C₂H₂ + MX. δA and δr are experimentally determined while the D_e values are calculated ab initio at the CCSD(T)(F12*)/AVTZ or AVDZ level of theory. The origin is included as a point under the assumption that zero interaction energy is associated with δA = 0 and δr = 0.

The nature of the ethyne distortions can be understood with the aid of a simple model. The nuclei of each of the C₂H₂⋯M–X (M = Cu or Ag, X = F or Cl) molecules all lie in the ab principal inertia plane. Let the symmetry plane of one of the ethyne π bonding orbitals lie in this plane, with that of the other π orbital perpendicular to it. When M–X approaches from large separation and takes up its position along a C₂ axis of ethyne (which then becomes the a axis of the new molecule), the partial positive charge δ+ that exists on the M atom in the species M–X (the metal halides have large electric dipole moments in the range ∼5 or 6 D)³⁵ polarizes electron density preferentially from the π orbital (π_ab) in the molecular plane. The larger the polarization, the more the π bonding in the ethyne molecule will resemble that of an ethene molecule in which the symmetry plane of its π bonding orbital is perpendicular to the ab plane and the C–H bonds lie in the ab plane. In the limit of very large polarization of the π_ab electrons, when both are completely removed from ethyne to yield the ion C₂H₂²⁺, the distortions would be of the order δA ≈ 60° and δr ≈ 134.5 − 120.6 = 13.9 pm, where 134.5 and 120.6 pm are the CC distances in the ground state ³Σ_g⁻ of the dication³⁶ C₂H₂²⁺ and in ethyne,²⁷ respectively. Similar distortions have been observed in C₂H₄⋯M–X (M = Cu or Ag),^6,37 in which M–X lies on the C₂ axis of C₂H₄ that is perpendicular to the plane of the C₂H₄ nuclei. Similar arguments can be used to rationalize the distortions in these molecules, but with C₂H₄²⁺ as the limiting dication.

Acknowledgements

We thank the European Research Council for postdoctoral fellowships awarded to D.P.Z. and S.L.S., and for project funding (CPFTMW-307000). ACL thanks the University of Bristol for a Senior Research Fellowship and Newcastle University for a Faculty of SAgE Visiting Professorship. D.P.Z. thanks Newcastle University for the award of a Faculty of SAgE Research Fellowship. D.P.T. gratefully acknowledges the award by the Royal Society of a University Research Fellowship.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5cp02248g

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